War planes

Logic Level 2

We are in war. Our planes go out on combat missions and often receive a good number of enemy shots. Sometimes they get back to base; Other times they are shot down. We are looking for a way to improve the situation. We can reinforce the outer surfaces to better resist shots, but the aircraft would be heavier, less maneuverable and would use up more fuel. It is best to reinforce only part of the plane. But, what part?

We are in war. Our plans go out on combat missions and often receive a good number of enemy shots. Sometimes they get back to base; Other times they are shot down. We are looking for a way to improve the situation. We can reinforce the outer surfaces to better resist shots, but the aircraft would be heavier, less maneuverable and would use up more fuel. It is best to reinforce only part of the plane. But, what part?

Engine: 11,95
Fuselage (central body): 18,62
Fuel system: 16,68
Rest of the plane: 19,38

Those numbers are the mean number of bullet holes per square meter.

So the question is: which area of the plane should we reinforce?

Rest of the plane Engine Fuel system Fuselage

2 solutions

Siva Budaraju
Jul 9, 2017

@Profe Ronald, I think this was inspired by Abraham Wald's WWII story. The excellent book How Not to be Wrong explains:

Correcto, it's a wonderful book !!!! Gives a very clear picture of how mathematics serves in the real world.

Ronald Chén - 3 years, 11 months ago

Phillip Temple
Jul 9, 2017

If the engine gets shot, even once, the damage is probably enough to take it down. A shot through a wing, however, might not. Therefore, it's logical to reinforce the weakest part of the plane: the engine. The other three options could survive a bullet without immediately and completely stopping the flight.

War planes

2 solutions

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